A constant force of 48.7 N, directed at 34.1° from horizontal, pulls a mass of 15.1 kg horizontally a distance of 2.77 m. Calculate the work done by the force.
48.7 cos 34.1 * 2.77 (Joules).
To calculate the work done by a force, you can use the formula:
Work = Force x Distance x cos(theta)
Where:
- Work is the amount of energy transferred by a force exerted over a distance.
- Force is the magnitude of the force applied.
- Distance is the displacement over which the force is applied.
- Theta (θ) is the angle between the force vector and the displacement vector.
In this case, the force is 48.7 N, the distance is 2.77 m, and the angle is 34.1°.
First, we need to find the horizontal component of the force using trigonometry. The horizontal component is given by:
Force horizontal = Force * cos(theta)
Substituting the given values, we get:
Force horizontal = 48.7 N * cos(34.1°)
Next, we can calculate the work using the formula:
Work = Force horizontal * Distance
Substituting the values, we have:
Work = (48.7 N * cos(34.1°)) * 2.77 m
Calculate the value of cos(34.1°):
cos(34.1°) ≈ 0.832
Work = (48.7 N * 0.832) * 2.77 m
Finally, we can calculate the work done:
Work ≈ 107.093 J (rounded to three decimal places)
Therefore, the work done by the force is approximately 107.093 J.